A straightforward example of this is shown for the metric \(g_{ij}(x)\) , which is a rank \((0,2)\)  tensor. Its Lie derivative is given by [1]}
\(£_{\delta \xi } g_{ij} = \partial _{k}g_{ij}\delta \xi ^{k}_{x} + g_{ik}\partial _{j}\delta \xi ^{k}_{x} + g_{kj}\partial _{i}\delta \xi ^{k}_{x}~.\) 
